Identifying a possible non-linear rule for a given table of values

Identifying a possible non-linear rule for a given table of values

Solution (substitution)

When x = 0, y = 1

One method of finding the correct answer is to try each of the options with a value of x. If an option does not give the correct y value it cannot be a correct response to the question.

The constant term is 1 which is the case for all the alternatives.

Option 1:	y = 1 − 2x²
	When x = −1
	y = 1 − 2 × (−1)² = 1 − 2 = −1 ≠ 3
Option 2:	y = 2x + 1
	When x = −1
	y = 2 × −1 + 1 = −2 + 1 = −1 ≠ 3
Option 3:	y = 2x² + 1
	y = 2 × (−1)² + 1 = 3, y = 2 × (−2)² + 1 = 9, y = 2 × (−3)² + 1 = 19
	Only one of the options is possible.

The answer is y = 2x² + 1.

Note: Using this method it might be necessary to try other values of x. It assumes that there is only one correct solution.

Identifying a non-linear rule

Further example, Q2